Smith numbers

Smith numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Smith numbers are numbers that the sum of the digits of the integers that make up that number is the same as the sum of digits of its prime factors excluding 1. The primes are also excluded as they, naturally, satisfy this condition!

Example: 166 => 2 x 83 => 2 + 8 + 3 = 1 + 6 + 6 = 13.

The task: write a program to find all Smith numbers below 10000.

C++

<lang cpp>

1. include <iostream>
2. include <vector>
3. include <iomanip>

void primeFactors( unsigned n, std::vector<unsigned>& r ) {

   int f = 2; if( n == 1 ) r.push_back( 1 );
   else {
       while( true ) {
           if( !( n % f ) ) {
               r.push_back( f );
               n /= f; if( n == 1 ) return;
           }
           else f++;
       }
   }

} unsigned sumDigits( unsigned n ) {

   unsigned sum = 0, m;
   while( n ) {
       m = n % 10; sum += m;
       n -= m; n /= 10;
   }
   return sum;

} unsigned sumDigits( std::vector<unsigned>& v ) {

   unsigned sum = 0;
   for( std::vector<unsigned>::iterator i = v.begin(); i != v.end(); i++ ) {
       sum += sumDigits( *i );
   }
   return sum;

} void listAllSmithNumbers( unsigned n ) {

   std::vector<unsigned> pf;
   for( unsigned i = 4; i < n; i++ ) {
       primeFactors( i, pf ); if( pf.size() < 2 ) continue;
       if( sumDigits( i ) == sumDigits( pf ) )
           std::cout << std::setw( 4 ) << i << " ";
       pf.clear();
   }
   std::cout << "\n\n";

} int main( int argc, char* argv[] ) {

   listAllSmithNumbers( 10000 );
   return 0;

} </lang>

Output:

   4   22   27   58   85   94  121  166  202  265  274  319  346  355  378  382
 391  438  454  483  517  526  535  562  576  627  634  636  645  663  666  690
...
9301 9330 9346 9355 9382 9386 9387 9396 9427 9483 9535 9571 9598 9633 9634 9639 
9648 9657 9684 9708 9717 9735 9742 9760 9778 9843 9849 9861 9880 9895 9975 9985

zkl

Uses the code (primeFactors) from Prime decomposition#zkl. <lang zkl>fcn smithNumbers(N=0d10_000){ // -->(Smith numbers to N)

  [2..N].filter(fcn(n){ 
     (pfs:=primeFactors(n)).len()>1 and
     n.split().sum(0)==primeFactors(n).apply("split").flatten().sum(0) 
  })

}</lang> <lang zkl>sns:=smithNumbers(); sns.toString(*).println(" ",sns.len()," numbers");</lang>

Output:

L(4,22,27,58,85,94,121,166,202,265,274,319,346,355,378,382,391, ...
3091,3138,3168,3174,3226,3246,3258,3294,3345,3366,3390,3442,3505, ...
9942,9968,9975,9985) 376 numbers